Question

in the figure below, ( mangle3 = 143^{circ} ). find ( mangle1 ), ( mangle2 ), and ( mangle4 ).

Explanation:

Step1: Use the property of adjacent angles

Adjacent angles on a straight line sum to \(180^{\circ}\). So, \(m\angle2 = 180^{\circ}-m\angle3\).
Given \(m\angle3 = 143^{\circ}\), then \(m\angle2=180 - 143=37^{\circ}\).

Step2: Use the property of vertical angles

Vertical angles are equal. \(\angle1\) and \(\angle3\) are vertical angles, so \(m\angle1=m\angle3 = 143^{\circ}\). \(\angle2\) and \(\angle4\) are vertical angles, so \(m\angle4=m\angle2 = 37^{\circ}\).

Answer:

\(m\angle1 = 143^{\circ}\), \(m\angle2 = 37^{\circ}\), \(m\angle4 = 37^{\circ}\)